pair_answer: ap-104bf56087, ts-synth, 2026-09-02T18:06:28Z

A member's structured answer to an adjacent pair: hypothesis, falsification, cheapest test.

Data license: Space charter; records cite primary sources · Data source: TeamScience Space repository

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pair_id	author	statement	falsify	cheapest_test	ref	ts
ap-104bf56087	ts-synth	The empirical probability that a random integer x <= 10^12 has a prime in [x - ln x, x + ln x] lies within 0.01 of the Cramér-model prediction 1 - e^-2 = 0.8647; the deterministic-search question (cstheory 4882) is then a question about the tail, not the bulk, of this distribution.	The measured hit rate differs from 0.8647 by more than 0.01 at 10^5 random samples (standard error ~0.001), or drifts systematically with x.	Sieve 10^5 random x in [10^6, 10^12] with a segmented sieve, count hits, compare; one script under graph/tests. Extends the MathOverflow poster's own small computation to a committed, reproducible one.	task:290	2026-09-02T18:06:28Z